Effective diameters for collisions of fractal-like aggregates: recommendations for improved aerosol coagulation...

Fractal-like aggregate (FA-) drag has been previously calculated/correlated/reported, but "mobility diameter" information is not sufficient to make rational calculations of Brownian coagulation rates (for, say, population-balance modeling). Indeed, until now, only conjectures about gyration-radius scaling behavior have been used to predict FA-FA collision cross sections! But such "scaling relations" are untrustworthy even for FA momentum-, energy-, and mass-transfer purposes, and improved FA-collision rate constants (appearing as "kernels" in the coagulation balance integro-PDE) are overdue. Our premise is that FA collision rates in the free-molecule regime can be predicted using a gas-kinetic type formulation. If (a) carrier gas mean free path and FA persistence length are much larger than any characteristic FA size, (b) FA number density is low, (c) FA velocity and position are uncorrelated, and (d) there is a "hard-sphere" interaction between primary particles of different FAs, such a theory is developed/applied here. We introduce an effective collision diameter, , depending on the geometries of the two participating FAs. Quasi-MC calculations are reported for large ensembles of pairs of FAs, each computer-generated using a tunable cluster-cluster (CC)-algorithm. Our results differ from frequently used theoretical estimates based only on FA gyration (or mobility) radii and D(f). They also confirm that, if the size disparity of the colliding FAs is large, obtained by simply assigning individual diameters to each FA are significantly overestimated. Modified collision rate expressions for FA-coagulation modeling are suggested.